Question

P (N) WE-4 A 3.00kg block is initially sliding to the right on a frictionless surface at 7.00m/s. Force P is directed to the left and is applied to the block continuously starting at the initial position as shown below. The magnitude of P varies as shown in the graph to the right. V-7.00m's 20 F 15 10 0 1 2 3 4(m) X. a) Find the magnitude of the work done by the force P as the block moves from x-0 to x-4m. b) Find the kinetic energy of the block at x-4m. Neglect air resistance (and the surface is frictionless). c) Find the speed of the block at x-4m. d) Has the speed increased or decreased? Has force P transferred energy to the block or from the block?

Answer 1

Magnitude of work done = Area under the force-displacement curve = Area of trapezium ABCDEA = 1/2 times (BC + AD) times BE = [1/2 times (5 + 20) times 4] Joule = (25 times 2) = 50 Joule kinetic energy of the block at x = 0 m, KE_i = 1/2 m v^2_i = 1/2 times 3 times (7)^2 Joule = 73.5 Joule Let KE_f be kinetic energy of block at x = 4 m, they by work-energy theorem, work done = change in kinetic energy w = KE_f - KE_i - 0 = -50 = KE_f - 73.5 (As P is opposite to x, so work is negative) KE_f = (50 + 73.5) J = 123.5 Joule therefore kinetic energy at x = 4m, KE_f = (73.5 - 50) J = 23.5 J If v_f be the speed of the block at x = 4m, then, KE_f = 1/2 m v^2_f = > v^2_f = 2 KE_f/m v_f = squareroot 2 KE_f/m = squareroot